The Avalanche have won back-to-back games for the first time in a month.
Weyne Simmonds brought the Flyers within a goal with 6:12 to go in the middle period but Varlamov slammed the door the rest of the way.
Philadelphia had won four straight, the last three to open a six-game road trip.
Steve Mason stopped 29 shots for the Flyers.
It was the third game of a seven-game homestand for Colorado, its longest of the season.
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